Typically you test your software to your needs. If there's a bug in a library you use it would show up when testing your code that uses the library.
> If there's a bug in a library you use it would show up when testing your code that uses the library. That's not true at all. You may catch some lib bugs, but not all, even through testing of your own code that leverages the lib. Unless you're implying that you'll pass every possible value to your tests which will then cover 100% of any and all code in the lib.
Your tests will be testing the parts of code in the library that your application uses, which is the part that matters to you.